Air Standard Cycle
#importing the math and matplotlib module
#math module is imported to perform mathematical functions
#matplotlib is used for plotting the results.
import math
import matplotlib.pyplot as plt
#creating a function to calculate the engine kinematics of the otto cycle with arguments.
def engine_kinematics(bore, stroke, con_rod, cr, start_crank, end_crank):
a = stroke/2 #crank pin radius
R = con_rod/a
#starting crank angle
sc = math.radians(start_crank)
#ending crank angle
ec = math.radians(end_crank)
#calculating swept volume and clearance volume using the parameters from arguments
v_s = math.pi/4 * pow(bore,2) * stroke
v_c = v_s/(cr-1)
#number of values of angles.
num_values = 50
#volume array
v = []
dtheta = (ec - sc)/(num_values-1)
#for loop to take different values of theta between starting crank angle and ending crank angle.
for i in range(0, num_values):
theta = sc + i * dtheta
#formulae to calculate the volume
term1 = 0.5 * (cr - 1)
term2 = R + 1 - math.cos(theta)
term3 = pow(pow(R,2) - pow(math.sin(theta),2),0.5)
#appending the values in the volume array
v.append((1 + term1 * (term2 - term3)) * v_c)
#returning the values in the function
return v
#inputs
p1 = 101325
t1 = 500
gamma = 1.4
t3 = 2300
#geometric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 12
#volume computation
v_s = (math.pi/4)*pow(bore,2)*stroke
v_c = v_s/(cr-1)
v1 = v_s + v_c
#state point 2
v2 = v_c
#p2v2^gamma = p1v1^gamma
p2 = p1 * pow(v1,gamma)/pow(v2,gamma)
#p2v2/t2 = p1v1/t1
rhs = (p1 * v1)/t1
t2 = (p2 * v2)/rhs
#calling the function and giving the parameters
v_compression = engine_kinematics(bore, stroke, con_rod, cr, 180, 0)
constant = p1 * pow(v1,gamma)
#calculating the p_compression for each v_compression value
p_compression = []
for v in v_compression:
p_compression.append(constant/pow(v,gamma))
#state point 3
v3 = v2
#p3v3/t3 = p2v2/t2
rhs = (p2 * v2)/t2
p3 = (rhs * t3)/ v3
#calling the function
v_expansion = engine_kinematics(bore, stroke, con_rod, cr, 0, 180)
constant = p3 * pow(v3,gamma)
#calculaing the p_expansion values for each v_expansion values
p_expansion = []
for v in v_expansion:
p_expansion.append(constant/pow(v,gamma))
#state point 4
v4 = v1
#p4v4^gamma = p3v3^gamma
p4 = (p3 * pow(v3,gamma))/pow(v4,gamma)
rhs = p3 * v3/t3
t4 = p4 * v4/rhs
#calculate the efficiency of the otto cycle
#efficiency = 1-((t4-t1)/(t3-t2)) = 1 - 1/(v1-(v2^(gamma-1)))
efficiency = float(1 - 1/(v1-(pow(v2,gamma-1))))
print(\"the efficiency of the otto cycle is \", efficiency)
#plotting the results.
plt.plot([v2, v3],[p2,p3])
plt.plot(v_compression, p_compression)
plt.plot(v_expansion, p_expansion)
plt.plot([v4,v1], [p4,p1])
plt.show()